The invention relates to a wing having a main wing part with a surface being circumflown in a closed manner and a wing grid arranged on a distal end of the main wing part. The wing preferably is the wing of an aerodynamic vehicle. The wing can, however, also be the wing of a propeller, the sail of a boat or the centerboard of a boat.
From the publications EP-0642440 and U.S. Pat. No. 5,823,480 of the same applicant, it is known to design the distal section of a wing as a wing grid comprising at least two winglets staggered in parallel in order to significantly reduce the induced drag of the complete wing as compared to a wing of the same wing span, but without a wing grid, or in order to achieve the same lift/drag ratio compared with a wing without wing grid and with a significantly greater wing span.
According to the above-mentioned publications, the following conditions must be fulfilled by the wing grid for the design point in order to achieve the named drag-reducing effect:
The lift per length unit of wing span (span load) is the same for the wing grid as for the main part of the wing (at least in the area in which the grid is attached to the main wing part; for a rectangular distribution of the lift if at all possible over the whole wing span) and the air flow around the main wing is taken over by the winglets of the wing grid along the chord section by section;
the winglets of the wing grid are staggered e.g. from the rear bottom to the front top, wherein the stagger angle (angle between the chord of the main wing part and the chord of the wing grid) is at least as great as the angle of attack of the main wing at the design point;
The winglets of the wing grid have an overlap, which is less than 1 (overlap=ratio between the winglet chord and the grid spacing).
If the conditions as mentioned above are fulfilled, the vortex discs coming away from the winglets of the grid flow off separately, such effecting the drag-reduction.
For a wing with a wing tip designed as a wing grid, for which the conditions mentioned above are fulfilled, the drag-reducing effect is a maximum in the design point. If this maximum effect is to be achieved for another angle of attack or for a different speed respectively, then the grid has to be correspondingly adjusted, for example by correspondingly adjusting the angle of attack of the individual winglets or by changing the chord lengths of the winglets. In the publications mentioned above, it is recommended for an adjustment of the angle of attack to have the wing grid to follow as a whole, wherein the grid parameters remain unchanged.
If, for the purpose of reducing the induced drag, a wing with a sweep as utilised for high sub-sonic speeds is equipped with a wing grid at its tip, then according to the above-mentioned publications the sweep not only of the main wing but also of the wing grid needs to be adapted to a predefined Mach number in function of the angle of attack and of the profile thickness. This may result in different sweep angles for the main wing and for the wing grid. It shows that a wing grid which is designed for an equal sweep angle produces a lift differing from that of the main wing and, therefore, usually has a smaller drag-reducing effect when used with a sweep angle that is different from the sweep angle of the main wing unless it is correspondingly modified or correspondingly adjusted.
It is an object of the invention to create a wing with a main wing part and a drag-reducing wing grid arranged at the distal end of the main wing part, for which wing the drag-reducing effect of the wing grid is fully maintained with changing angle of attack without the wing grid having to be adjusted or made to follow.
For achieving this object, the main wing part and wing grid of the wing according to the invention have to fulfil the above mentioned conditions regarding overlap and stagger angle as well as the condition of producing the same lift (CL) in the design point. In addition, the main wing part and the wing grid also have to be designed to have an essentially equal lift gradient (xcex4CL/xcex4xcex1 or lift change per change of the angle of attack xcex1).
It can be shown, that the conditions mentioned with respect to lift and lift gradient can be simultaneously fulfilled, if the average zero air flow direction of the winglets of the wing grid is essentially the same as the zero air flow direction of the main wing and if the chord length of the grid is adapted to the chord length of the main wing part in function of the overlap of the winglets such that the ratio of the chord length of the main wing part to the chord length of the grid in essence is the same as the correction factor Kappa according to Betz applicable for the average overlap of the winglets (refer to FIG. 3).
To be understood by coincidence of the zero air flow direction of main wing part and wing grid is the fact that the grid is to be arranged on the main wing such that, in case of an incidence of the main wing part relative to an air flow, no lift results (zero angle of attack), the grid does not produce a lift. To be understood by chord length of the grid, is the distance between the front edge of the foremost winglet in the direction of the air flow to the rear edge of the rearmost winglet in the direction of the air flow. The average overlap is the ratio of the average chord length of the winglets and the average grid spacing.
For a wing, the main wing part and wing grid of which fulfil the above-mentioned conditions, the lift for the main wing part and for the wing grid is always the same independent of the angle of attack. This also signifies that the wing grid maintains its drag-reduction effect independent of the angle of attack. This can be attributed to the fact that both wing parts have the same deflection characteristics, as a result of which upon a change of the angle of attack, the lift changes by the same amount for the main wing part and for the wing grid (same lift gradient).
The statement of the previous paragraph is exactly true only for a case in which the wing grid does not have any lift-dependent twisting effect on the main wing.
For adapting a drag-reducing wing grid with at least two winglets and an overlap  less than 1 to a predefined main wing part with a predefined profile and, therefore, a predefined lift and a predefined lift gradient, the cross-section of the wing grid is enlarged affinely such that the chord length of the grid is adapted to the chord length of the main wing part in the manner mentioned above. This adapted grid is arranged on the main wing part such that the stagger angle is greater than the angle of attack of the main wing part in the design point and the angle of attack of the winglets is adapted for the coincidence of the zero air flow of main wing part and wing grid.
In order to avoid twisting of the wing part by the wing grid, the grid furthermore is advantageously arranged on the main wing part such that its center of lift is located on the elastic torsion axis of the main wing part. This is achieved by correspondingly positioning the wing grid on the main wing. If so required, the position of the center of lift of the grid can also be adjusted for a predefined grid position on the main wing part, by adapting the lift distribution in the grid correspondingly or by sweeping the grid (only for Mach numbers below 0.5).
It can be shown that the adaptation of the drag-reducing grid located at the tip of a wing in accordance with the invention to different Mach numbers or to different sweep angle differences between main wing part and wing grid can be realized by means of a simple affine size change of the grid cross section. In doing so, the cross section of the wing grid, while maintaining the relevant grid parameters, is dimensioned such that the ratio of the chord length of the main wing part to the chord length of the wing grid is corrected by the inverse ratio of the cosine of the two sweep angles, this in addition to the above mentioned adaptation based on the deflection characteristics. For a wing in accordance with the invention, which is swept back, therefore the ratio of the chord length of the main wing part to the chord length of the wing grid corresponds to the above mentioned correction factor Kappa according to Betz multiplied with the inverse ratio of the cosines of the sweep angles.
For a wing according to the invention without sweep, therefore, for the ratio of the chord lengths of the main wing part and wing grid, the following is applicable:
cM/cW=Kappa (c/t)
For a wing according to the invention with sweep:
cM/cW=Kappa (c/t) x cos xcfx86W/cos xcfx86M 
wherein:
cM=chord length of the main wing part,
cW=chord length of the wing grid (distance from t he front edge of the foremost winglet to the back edge of the rearmost winglet),
Kappa=correction factor according to Betz, dependent on overlap and deflection angle,
c=chord length of the winglets
t=grid spacing
c/t=overlap
cos xcfx86M=cosine of sweep angle of main wing part,
cos xcfx86W=cosine of sweep angle of grid.
The ratio of the chord length of the main wing part to the chord length of the wing grid advantageously deviates from the values demanded in the previous paragraphs by less than 10%. The coincidence of the zero airflow direction is advantageously better than 2xc2x0.